Hmmm i dont understand what u mean here. Thing is forget about constants and then solve the equation. Assuming lets say there are no constants then how do you solve the equation. Technically it should give me two normal equations.

Why choose zeor for w and x. We have to minimize the equation for w and x and as far as i know the way was to take derivative with respect to each unknown vector and put it equal to zero and then solve the equation. This should give two normal equations. First take derivative with respect to x and put equal to zero and then take derivative with respect to w and put equal to zero. Thats what i think.

I actually was looking for an answer for a generalized case. So that is why i am saying that there could be any arbitrary values for G and M and values of w and x are to be found so you cannot just assume that they have zero value.

What I was trying to say was that the function to be minimized is the second norm of a vector so its smallest possible value is zero. Now if we do not have the constant component constraints then we can choose x=w=0 and achieve this minimum. So (0,0) is our solution.

Now if we have the constant constraints then the above posted solution seems to be completely general. The only thing I have done is taken the variable components of x (named it x_2) and y and made them a single vector of a higher dimension. And the problem reduces to a standard least square in this higher dimensional space.